Simulation of combustion of methane-air mixture in two-dimensional approximation

Abstract The paper presents a mathematical model and the results of a numerical study of the flame propagation of a methane-air mixture. The physical and mathematical formulation of the problem takes into account the thermal expansion of the gas and its subsequent movement. The problem was solved numerically using the Van Leer method to determine the fluxes at the boundaries of the computational cells. A study of flame propagation in a methane-air mixture with a methane content less than or equal to stoichiometric has been carried out. The conditions for focal ignition of a reactive mixture are determined. The influence of the channel walls on the features of flame propagation is shown. The necessity of taking into account the non-isobaricity of the combustion process at the initial stage is demonstrated.

Download Full-text

Numerical Simulation of Premixed Propane/Air Flame Propagation Using a Dynamically Thickened Flame Approach

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.444-445.1574 ◽

2013 ◽

Vol 444-445 ◽

pp. 1574-1578 ◽

Cited By ~ 1

Author(s):

Hua Hua Xiao ◽

Zhan Li Mao ◽

Wei Guang An ◽

Qing Song Wang ◽

Jin Hua Sun

Keyword(s):

Numerical Simulation ◽

Flame Propagation ◽

Numerical Study ◽

Vortex Motion ◽

Combustion Process ◽

Single Step ◽

Premixed Combustion ◽

Premixed Flame ◽

Flame Surface ◽

Arrhenius Kinetics

A numerical study of premixed propane/air flame propagation in a closed duct is presented. A dynamically thickened flame (TF) method is applied to model the premixed combustion. The reaction of propane in air is taken into account using a single-step global Arrhenius kinetics. It is shown that the premixed flame undergoes four stages of dynamics in the propagation. The formation of tulip flame phenomenon is observed. The pressure during the combustion process grows exponentially at the finger-shape flame stage and then slows down until the formation of tulip shape. After tulip formation the pressure increases quickly again with the increase of the flame surface area. The vortex motion behind the flame front advects the flame into tulip shape. The study indicates that the TF model is quite reliable for the investigation of premixed propane/air flame propagation.

Download Full-text

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

Heat Transfer, Volume 2 ◽

10.1115/imece2004-60294 ◽

2004 ◽

Author(s):

K. M. Akyuzlu ◽

Y. Pavri ◽

A. Antoniou

Keyword(s):

Mathematical Model ◽

Stokes Equations ◽

Numerical Study ◽

Vertical Wall ◽

Ideal Gas ◽

Working Fluid ◽

Two Dimensional ◽

Algebraic Equations ◽

Rectangular Enclosure ◽

Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Download Full-text

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: Transition From Laminar to Turbulent Flow

Volume 7: Fluid Flow, Heat Transfer and Thermal Systems, Parts A and B ◽

10.1115/imece2010-37892 ◽

2010 ◽

Author(s):

K. M. Akyuzlu ◽

M. Chidurala

Keyword(s):

Mathematical Model ◽

Finite Difference ◽

Turbulent Flow ◽

Numerical Study ◽

Second Order ◽

Working Fluid ◽

Two Dimensional ◽

Rectangular Enclosure ◽

Circulation Patterns ◽

Vertical Walls

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature stratification inside a rectangular enclosure. One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for turbulent compressible flows), and energy equations for the enclosed fluid subjected to appropriate boundary conditions. A standard two equation turbulence model is used to model the turbulent flow in the enclosure. The compressibility of the working fluid is represented by an ideal gas relation. The conservation equations are discretized using an implicit finite difference technique which employs second order accurate central differencing for spatial derivatives and second order (based on Taylor expansion) finite differencing for time derivatives. The linearized finite difference equations are solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Numerical experiments were then carried out to simulate the development of the buoyancy driven circulation patterns inside rectangular enclosures (with aspects ratios 0.5, 1 and 1.5) filled with a compressible fluid (Pr = 0.72). Experiments were repeated for various wall temperature differences which corresponded to Rayleigh numbers between 104 and 106. Changes in unsteady circulation patterns, temperature contours, and vertical and horizontal velocity profiles were predicted while the flow inside the enclosure transferred from laminar to turbulent flow due to the sudden temperature change imposed on the vertical walls of the enclosure. Only the results of the enclosure with aspect ratio one is presented in this paper. These results indicate that this transition is characterized by unicellular circulation patterns breaking up in to multicellular formations and increase in the values of the predicted wall heat fluxes and Nusselt number as flow becomes turbulent.

Download Full-text

Numerical study of the effects of laminar flame speed on flame dynamics in the early stages of flame propagation in two-dimensional half open tubes

International Journal of Hydrogen Energy ◽

10.1016/j.ijhydene.2020.09.226 ◽

2021 ◽

Vol 46 (1) ◽

pp. 1288-1301

Author(s):

Haoxin Deng ◽

Zhifeng Yao ◽

Guoyan Chen ◽

Xiaoping Wen ◽

Fahui Wang ◽

...

Keyword(s):

Flame Propagation ◽

Laminar Flame ◽

Numerical Study ◽

Flame Speed ◽

Laminar Flame Speed ◽

Two Dimensional ◽

Early Stages ◽

Flame Dynamics

Download Full-text

Numerical study of a two-dimensional mathematical model with variable heat exchange coefficient which arises in cryosurgery

Journal of Applied and Industrial Mathematics ◽

10.1134/s1990478917040056 ◽

2017 ◽

Vol 11 (4) ◽

pp. 494-499

Author(s):

B. K. Buzdov

Keyword(s):

Mathematical Model ◽

Heat Exchange ◽

Numerical Study ◽

Two Dimensional ◽

Exchange Coefficient ◽

Heat Exchange Coefficient ◽

Variable Heat

Download Full-text

Asymptotic and numerical study of variable-density premixed flame propagation in a narrow channel

Journal of Fluid Mechanics ◽

10.1017/s0022112009990966 ◽

2009 ◽

Vol 638 ◽

pp. 305-337 ◽

Cited By ~ 24

Author(s):

MARK SHORT ◽

DAVID A. KESSLER

Keyword(s):

Thermal Expansion ◽

Flame Propagation ◽

Peclet Number ◽

Numerical Study ◽

Narrow Channel ◽

Variable Density ◽

Constant Density ◽

Closed Channel ◽

Péclet Number ◽

Variable Density Flow

The influence of thermal expansion on the dynamics of thick to moderately thick premixed flames (flame thickness less than or comparable to the channel height) for a variable-density flow in a narrow, rectangular channel is explored. The study is conducted within the framework of the zero-Mach-number, variable-density Navier–Stokes equations. Both adiabatic and non-adiabatic channel walls are considered. A small Péclet number asymptotic solution is developed for steady, variable-density flame propagation in the narrow channel. The dynamics of channel flames are also examined numerically for O(1) Péclet numbers in configurations which include flame propagation in a semi-closed channel from the closed to the open end of the channel, flame propagation in a semi-closed channel towards the closed end of the channel and flame propagation in an open channel in which a Poiseuille flow (flame assisting or flame opposing) is imposed at the channel inlet. Comparisons of the finite-Péclet-number dynamics are made with the behaviour of the small-Péclet-number solutions. We also compare how thermal expansion modifies the flow dynamics from those determined by a constant-density model. The small-Péclet-number variable-density solution for a flame propagating in a circular pipe is given in the Appendix.

Download Full-text

NON-UNIFORM SUSPENDED SEDIMENTS UNDER WAVES

Coastal Engineering Proceedings ◽

10.9753/icce.v21.84 ◽

1988 ◽

Vol 1 (21) ◽

pp. 84

Author(s):

Aronne Armanini ◽

Piero Ruol

Keyword(s):

Experimental Data ◽

Boundary Layer ◽

Mathematical Model ◽

Mathematical Formulation ◽

Suspended Sediments ◽

Two Dimensional ◽

Different Diameters ◽

Wave Boundary ◽

The Mathematical Model ◽

Dimensional Wave

An original mathematical formulation for suspended sediments in a two-dimensional wave boundary layer is presented. The model accounts for non-immediate adaptation of sediments to the hydrodinamic conditions, and allows to include the effect of sorting of the different diameters considered. The mathematical model is numerically solved through a finite difference scheme. It is suitable that results compare favourably with experimental data by Staub et alii.

Download Full-text