BY : Dr S V Zhubrin, CHAM Ltd

DATE : December, 2001

FOR : Demonstration case for V3.4

The application of an Eddy-Dissipation Model of Magnussen and Hjertager blended with Arrhenius-type reaction rates is presented aimed at the demonstration of the method for the simulation of the two-step turbulent combustion in some typical burner design.

Special attention is given to NOX formation by incorporating the simple realistic model for the rate of the oxidation of atmospheric nitrogen present in the combustion air. It is known as the steady-state simplification of Zeldovich mechanism with partial-equilibrium assumptions.

The present example consists of an plane-symmteric burner in which methane burns in a stream of heated air. The fuel and oxidant are introduced through separate streams into the burner. The fuel enters through a duct on the symmetry plane of the burner, and the air is introduced through an annual inlet into a chamber surrounding the fuel duct. Therein, the air is divided in two streams: one of them, primary air, is injected straight into the fuel stream, with the remaining, secondary, air being supplied through the orifice into the downstream recirculation region as depicted here.

The fuel is ignited on entry and steady combustion is in progress producing the high temperature combustion products.

The task is to calculate the temperatures and composition of combustion gases along with all related flow properties.

The independent variables of the problem are the two components of cartesian coordinate system, namely X and Y.

The main dependent (solved for) variables are:

- Pressure, P1
- Two components of velocity, U1 and V1,
- Turbulence energy and its dissipation rate, KE and EP,
- Gas specific enthalpy, H1,
- Mass fractions of gas mixture, namely, fuel methane (YCH4), oxygen (YO2), carbon monoxide (YCO), water vapour (YH2O), carbon dioxide (YCO2), nitrogen (YN2) and nitric oxides, collectively reffered to as (YNOX).

Although, the transport equations are usually solved for all of these variables, the nitric oxides are supposed to be presented only in trace quantities non-contributing to the state of the gas mixture and mass conservation.

The standard K-epsilon model, KEMODL, is used to calculate the distribution of turbulence energy and its dissipation rate from which the turbulence viscosity is deduced.

Combustion is treated as a two-step irreversible chemical reaction of methane oxidation as follows:

Step 1: CH_{4} + 1.5 ( O_{2} + 3.76N_{2}) =
CO + 2H_{2}O + 5.64N_{2}

Step 2: CO + 0.5( O_{2} + 3.76N_{2} ) = CO_{2} +
1.88N_{2}

The reaction rates of combustion are obtained as the limiting blend of a Arrhenius kinetics and eddy-dissipation rates:

R^{com}_{CH4} = - min ( R^{k}_{CH4},
R^{e}_{CH4} ) and

R^{com}_{CO} = - min ( R^{k}_{CO}, R^{e}_{CO} ),

where R^{k} and R^{e}, in kg/m^{3}s, are the kinetic and eddy-dissipation rates:

R^{e}_{CH4} = 4 RHO1 EP/KE min( YCH4, YO2/3)

R^{e}_{CO} = 4 RHO1 EP/KE min( YCO, YO2/0.57)

R^{k}_{CH4} =
1.15 10^{9}RHO1^{2}e^{-24444/T}
YCH4^{-0.3}YO2^{1.3}

R^{k}_{CO} =
5.42 10^{9}RHO1^{2}e^{-15152/T}
YO2^{0.25}YH2O^{0.5}YCO

The remaining rates are defined through associated stoichiometric coefficients:

__Step 1:__

R^{1}_{O2} =
3 R^{com}_{CH4}

R^{1}_{CO} =
-1.75 R^{com}_{CH4}

R^{1}_{H2O} =
-2.25 R^{com}_{CH4}

__Step 2:__

R^{2}_{O2} =
0.57 R^{com}_{CO}

R^{2}_{CO2} =
-1.57 R^{com}_{CO}

The net rates of species generation, i.e. the source terms, are the balances of formation and combustion as appropriate:

S_{CH4} = R^{com}_{CH4}

S_{CO} = R^{com}_{CO} +
R^{1}_{CO}

S_{O2} = R^{1}_{O2} +
R^{2}_{O2}

S_{CO2} = R^{2}_{CO2}

S_{H2O} = R^{1}_{H2O}

The NOX formation rate, in kg/m^{3}/s, is given by:

S_{NO} = 2 RHO1 K_{1} YN2 [O] M_{NO}/
M_{N2}

where M_{NO} = 30, is NO molecular mass,

M_{N2} =28, is N_{2} molecular mass, and,

K_{1} = 1.8 10^{8}e^{-38370/T},

stands for the reaction-rate constant for the forward
reaction:

N_{2} + O --> NO +H

The equilibrium O-atom concentration, [O], can be obtained from the expression:

[O] = 3.97 10^{5}T^{-0.5}(RHO1 YO2/M_{O2})
^{0.5}e^{-31090/T}

wherein M_{O2} =32, is the molecular mass of oxygen.

The gas density is computed from the ideal-gas law.

The specific enthalpies are related to gas temperatures and specific heat:

H1 = C_{P}T

The specific heat, C_{P}, is assumed to be equal for all gas components and is a function of temperature as follows:

C_{P} = 1059 + 0.25( T - 300 )

The constant reaction heats, i.e. the heats of combustions for fuel methane,
H°_{CH4}, and carbon monoxide, H°_{CO}, are
released with the rates of their consumptions. In terms of the transport
equation for H1, the source term for specific enthalpy, in J/s, due to combustion of
CH_{4} and CO is:

S_{H1} = R^{com}_{CH4}H°_{CH4} +
R^{com}_{CO}H°_{CO}

Uniform velocities, air and fuel temperatures are assumed at the burner inlets, and the pressure is assumed constant at the outlet plane.

The pure methane, YCH4=1, enters its inlet and dry air, YN2=0.768, YO2=0.232, enters the oxidant inlet.

At the walls, standard "wall-functions" are used for the gas velocities, and the condition of zero flux is assumed for enthalpy and mass fractions.

The plots show the distribution of temperatures, velocities and other related fields within the burner.

Pictures are as follows :

- Burner geometry and velocity vectors
- Temperature contours
- NOX mass fraction contours
- CH4 mass fraction contours
- O2 mass fraction contours
- N2 mass fraction contours
- CO2 mass fraction contours
- CO mass fraction contours
- H2O mass fraction contours
- Volumetric rates of CH4 combustion
- Volumetric rates of CO combustion
- Volumetric rates of NOX formation

All model settings have been made by PIL commands and PLANT settings of PHOENICS 3.4