numerical modeling of turbulent diffusion flame using finite-rate chemistry model

Copyright © 2007 by M. Hejazi 1

Numerical Modeling of Turbulent Diffusion Flame Using Finite-Rate Chemistry Model

Matt M. Hejazi

Department of Mechanical Engineering Florida Atlantic University

777 Glades Rd. Boca Raton, FL, 33431

ABSTRACT

The work in this project is focused on simulation of a turbulent diffusion flame in a cylindrical combustor, using finite-rate chemistry model, in which, effect of fuel-inlet velocity, air-inlet temperature and different oxygen concentration was tested. For this test, a segregated solver and a combustion model for turbulent diffusion flame was utilized. The results obtained revealed that by increasing the flame`s oxygen concentration, the NOx emission will increase. INTRODUCTION

The numerical modeling is focused on the use of the random vortex method to treat turbulent flow fields associated with combustion while flame fronts are considered as interfaces between reactants and products, propagating with the flow and at the same time advancing in the direction normal to themselves at a prescribed burning speed. The first step in solving any problem involving species transport and reacting flow is to determine which model is appropriate, since this reacting system involves turbulent diffusion flame that are near chemical equilibrium, for the purpose of this project, the non-premixed combustion model in an axisymmetric domain for turbulent diffusion flame in a cylindrical combustor was utilized. Fuel-inlet velocity, air-inlet temperature and oxygen concentration, play an important role when designing practical combustion devices. The relatively simple Eddy Dissipation Concept (EDC) has proven to describe turbulent combustion well [2] and has the flexibility to describe chemical kinetics in a detailed manner. EDC is implemented in the general-purpose CFD code. Results from numerical simulations of a turbulent diffusion flame of methane are presented. GOVERNING EQUATION The species transport equation is as follows: Where Ri is the net rate of production by chemical reaction and Si is the rate of creation by addition from the dispersed phase plus any user-defined sources. Mass diffusion in turbulent flows is given by:

Where Sct is the turbulent Schmidt number, μt/ρDt The eddy-dissipation model computes the rate of reaction under the assumption that chemical kinetics are fast compared to the rate at which reactants are mixed by turbulent fluctuations. In all the simulations a standard model and a finite rate chemistry model has been used. Temperature, flow, continuity and momentum equations could be found in Fluent user guide hand book.

NUMERICAL METHOD The numerical method utilized for the simulation had a pressure based solver with implicit formulation, axisymmetric domain geometry, absolute velocity formulation, and superficial velocity for porous formulation. The green-gauss cell based was used for the gradient option. There are different equations used for flow, turbulence, species, and energy. A simple method was used for the pressure-velocity coupling. For the discretization, a standard pressure was used, and momentum, turbulent kinetic energy, turbulent dissipation rate, species, and energy was set to first order upwind. PROBLEM DESCRIPTION A small nozzle in the center of a cylindrical combustor introduces methane at 80 m/s. The ambient air enters the combustor coaxially at 0.5 m/s. The flame considered is a turbulent diffusion flame. The overall equivalence ratio is approximately 0.76 (~ 28% excess air). The high speed methane jet initially expands with little interference from the outer wall, and entrains and mixes the low speed air. The Reynolds number based on the methane jet diameter is approximately 5.7 x 103. The following combustion simulation cases are considered to be carried out:

I) CH4/air flame: (a) Solve the combustion simulation of methane/air with variable specific heat (Cp), and (b) plot the contours of static temperature, velocity magnitude, the velocity vectors, and CH4 , O2, CO2 mass fractions, and (c) plot the contours of NOx production (thermal + prompt).


RESULTS After solving the simulation combustion the contours of

static temperature, velocity magnitude are shown in plot 1-a and 1-b respectively.

Plot 1-a Static Temperature (k)

Plot 1-b Velocity Magnitude (m/s)

As shown above, plot 1-a demonstrates the air temperature contour and its increase along the cylindrical combustor. Plot 1-b, shows the decrease of the velocity magnitude as the high speed jet initially expands with little interference from the outer wall and entrains and mixes the low speed air.

Plot 1-c Velocity Vectors

The velocity vectors are also shown in plot 1-c, in which colored by the magnitude and the direction of the velocity magnitude.

The mass fraction of CH4, O2 and CO2 is shown in plots 1-d thru 1-f. It is clear that as the jet is introduced by the small nozzle in the center of the cylindrical combustor, a decreasing trend of the mass fraction over the distance within the combustor could be observed.

Plot 1-d Mass Fraction of CH4

Above is the mass fraction contour of the CH4 along the combustor is demonstrated. It starts off with value of 1.00 in the red color region and as it gets far away its concentration will drop.


Plot 1-e Mass Fraction of O2

As it is shown in plot 1-d, the amount of oxygen that

was inputted in the program (0.21) is at its maximum value at the very left hand side as it is enters the combustor coaxially, and its concentration will decrease as it gets far away from the nuzzle in the cylindrical combustor.

Plot 1-f Mass Fraction of CO2

It could be observed, CO2 distribution is exactly at the position of the flame. The blue represents the region with zero CO2 concentration and as it turns into the yellow and red color its concentration increases. NOx emission is coming from the oxygen, and nitrogen in the air at high temperature.

Plot 1-g NOx Production (thermal + prompt)

Figure 1-a Grid and Geometry

In the figure 1-a, the geometry and number of the grid is shown. Since the geometry in this case was symmetric, only half of the cylinder was considered for the simulation model.

II) Combustion with Different Fuels: (a) Solve the combustion simulation of ethane (C2H6) and propane (C3H8) fuels in air with the same conditions, and (b) Compare the temperature and NOx production (prompt + thermal) distribution at X = 1.0 m and X = 1.8 m (exit of the combustor) for the CH4/air, C2H6/air, and C3H8/air flames

RESULTS


After solving the simulations for the fuels and air combustions, the contours of air temperature and NOx production distribution at X=1.0m (middle) and X=1.8m (exit of the combustor) are as follows:

Plot 2-a Ethane (C2H6)/Air-NOx Production

Plot 2-b Ethane (C2H6)/Air-Temperature

The NOx emission of ethane fuel is shown on plot 2-a and the static temperature plot is shown on plot 2-b.As it could be observed, the NOx mass fraction distribution from the axis to the wall of the combustor is along the x-axis and as it gets far away from the exit, is along the y-axis.

The shift in the peaks could be observed by following the red plot (middle), and black plot (exit of the combustor) along the radial and lateral distance of the cylindrical combustor.

Plot 2-c Propane (C3H8)/Air-NOx Production

Plot 2-d Propane (C3H8)/Air-Temperature


Plot 2-e Methane (CH4)/Air-NOx Production

Plot 2-f Methane (CH4)/Air-Temperature By comparing the plots among the three fuels, it could be observed that the NOx emission of all the fuels at the exit of the combustion is at its peak value and for the air temperature is the same.

III) Effect of air temperature: (a) Solve the combustion simulation of methane/air flame with different air temperature (400, 500, 600 K), and (b) Compare the temperature and NOx production (prompt + thermal) distribution at X = 1.0 m and X = 1.8 m

(exit of the combustor) with different air temperature

RESULTS

After solving the simulations for the methane/air combustions with different air temperature, and NOx and temperature production distribution at X=1.0m (middle) and X=1.8m (exit of the combustor), the following results are obtained:

Plots 3-a thru 3-f are the contours of the simulation for the combustion model at 400, 500 and 600 °K.

Plot 3-a CH4/Air- Temperature @ 400°k

Plot 3-a shows the temperature distribution of methane-air combustion at 400°k. Plot 3-b shows the NOx distribution of the methane-air combustion at the same temperature; by looking at the plot, the shift of the peak value could be observed.


Plot 3-b CH4/Air- NOx Production @ 400°k

Plot 3-c CH4/Air- Temperature @ 500°k

Plot 3-d CH4/Air- NOx Production @ 500°k By looking at the temperature distribution plot it is clear that the peak temperature value is at the exit of the combustion shown in plot 3-d. The maximum NOx distribution at 500°k is also at the exit of the combustion shown in the plot 3-d.

Plot 3-e CH4/Air- Temperature @ 600°k


Plot 3-f CH4/Air- NOx Production @ 600°k As shown in the plots 3-e and 3-f, the peak value of the temperature distribution and NOx emission of the combustion happens at the exit of the combustion. The simulation model with 600°k-air temperature only seems to have a highest air temperature in the middle rather than exit of the combustion among the other two models at the beginning of the combustion. At the exit of the combustion, the model at 500°k air temperature seems to have the highest peak air temperature.

IV) Effect of oxygen concentration: (a) Solve the combustion simulation of methane/air flame with different oxygen concentration (21, 25, 30, 35%), and (b) Compare the temperature and NOx production (prompt + thermal) distribution at X = 1.0 m and X = 1.8 m (exit of the combustor) with different oxygen concentrations.

RESULTS

After solving the simulations for the methane/air combustions with different oxygen concentration and NOx production and temperature distribution at X=1.0m (middle) and X=1.8m (exit of the combustor), the following results are obtained:

Plots 4-a thru 4-i are the contours of the simulation for the combustion model with different oxygen concentration.

Plot 4-a CH4/Air- NOx Production-21% O2

Plot 4-a demonstrates the NOx distribution of the 0.21 O2 methane-air combustion. The shift in the peaks could be observed by following the blue plot (middle), and black plot (exit of the combustor) along the radial and lateral distance of the cylindrical combustor. The plot for air temperature contour is shown on the plot 4-b, in which, it is observed that the peak value of the air temperature is at X=1m (middle of combustion). The plots for other simulation models with 30% and 35% oxygen concentration are as following page.

Plot 4-b CH4/Air- Static Temperature- 21% O2


Plot 4-c CH4/Air- NOx Production - 25% O2

Plot 4-d CH4/Air- Static Temperature- 25% O2

Plot 4-e CH4/Air- NOx Production - 30% O2

Plot 4-f CH4/Air- Static Temperature- 30% O2


Plot 4-g CH4/Air- NOx Production - 35% O2

Plot 4-h CH4/Air- Static Temperature- 35% O2

As shown in the plots above, among the contours of

static temperature distributions, the peak value of the temperature distribution is at X=1.0m ( middle) section in 21% and 25% O2 concentration models and in 30% and 35% O2 concentration models, the peak value of the air temperature is at X=1.8m (exit of combustion) despite the other two. On the other hand, only in 25% O2 concentration model, the peak value of NOx emission of the combustion is at the middle of the combustion despite the other models.

V) Effect of turbulence intensity: (a) Solve the combustion simulation of methane/air flame with different turbulence intensity (5, 10, 15%), and (b) Compare the temperature, velocity magnitude, turbulence kinetic energy, and NOx production (prompt + thermal) distribution at X = 1.0 m and X = 1.8 m (exit of the combustor).

RESULTS After solving the simulations for the methane/air

combustions with different turbulence intensity and NOx production, velocity magnitude and temperature distribution at X=1.0m (middle) and X=1.8m (exit of the combustor), the following results are obtained: Plots 5-a thru 5-I are the contours of the simulation for the combustion model with different turbulence intensity.

Plot 5-a CH4/Air- Static Temperature- 5% T.I.


Plot 5-b CH4/Air- NOx Production - 5% T.I. As it is shown, the peak value of the air temperature and the NOx emission is at X=1.0m (middle) section of the combustion.

Plot 5-c CH4/Air- Turbulent Kinetic Energy - 5% T.I.

Plot 5-d CH4/Air- Velocity Magnitude - 5% T.I. Based on the plots above, the peak value for temperature distribution and NOx production is at X=1.0 (middle), and the turbulence kinetic energy and velocity magnitude are higher at the exit of the combustion.

Plot 5-e CH4/Air- Static Temperature- 10% T.I.


Plot 5-f CH4/Air- NOx Production - 10% T.I.

Plot 5-g CH4/Air- Turbulent Kinetic Energy - 10% T.I.

Plot 5-h CH4/Air- Velocity Magnitude - 10% T.I.

Plot 5-i CH4/Air- Static Temperature- 15% T.I.


Plot 5-j CH4/Air- NOx Production - 15% T.I.

Plot 5-k CH4/Air- Turbulent Kinetic Energy - 15% T.I.

Plot 5-l CH4/Air- Velocity Magnitude - 15% T.I. For the methane-air flame with different turbulence intensity, it could be observed that the NOx mass fraction distribution from the axis to the wall of the combustor is along the x-axis and as it gets far away from the exit, is along the y-axis. The shift in the peaks could be observed by following the red plot (middle), and black plot (exit of the combustor) along the radial and lateral distance of the cylindrical combustor. CONCLUSION AND DISSCUSION The primary focus of this project was on simulation of a turbulent diffusion flame in a cylindrical combustor, using finite-rate chemistry model ( ), in which, effect of fuel-inlet velocity, air-inlet temperature and different oxygen concentration was tested. For this test, a segregated solver and a combustion model for turbulent diffusion flame was utilized. Since the Cp was not constant, we didn’t have over prediction of the temperature distribution in our simulations. The results obtained revealed that by increasing the flame`s oxygen concentration, the NOx emission will increase.


REFERENCES [1] S.R. Turns, “An Introduction to Combustion: Concepts and Applications”, McGraw-Hill Publishing Co.; 2nd Rev. Ed edition March, 2000. [2] I. R. Gran. Mathematical Modeling and Numerical Simulation of Chemical Kinetics in Turbulent Combustion. Dr. ing. thesis, University of Trondheim, 1994. [3] Ghoneim, A.F. ; Chorin, A.J. ; Oppenheim, A.K., “Numerical modeling of turbulent combustion”, California Univ., Berkeley, March, 1983

numerical modeling of turbulent diffusion flame using finite-rate chemistry model

Documents