By : Dr S V Zhubrin, CHAM Ltd
Date : December 2001
For : Case study of MFM-CVA
A Multi-Fluid Model is applied to steady-state flow, heat and mass transfer in some typical burner design. The special attention is given to pollutant formation of carbon monoxide and nitric oxides.
The ability to predict the two-step chemical reactions in a turbulent flows by way of MFM is a motivation of this work. Therefore the objectives of the study are: (a) To formulate the MFM describing the important reaction phenomena involved; (b) to incorporate them in PHOENICS; (c) to compare the results with single-fluid predictions; and (d) to investigate the physical realism of the results obtained.
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 five-fluid population is introduced to represent the actual gas mixture, in which the 5th fluid is associated with inlet fuel-bearing material while the 1st one is considered to be the inlet oxidant substance. The remaining fluids represent the intermediate states uniformly distributed over the population space. The micromixing factor, Cmix, is supposed to be constant and equal to 10.
The within-fluid properties form the set of CVA, Continuously-Varying Attributes, for each fluid, which are solved along with APA, All-Population Attributes, and FMF, Fluid Mass Fractions.
The dependent (solved for) variables are:
The transport equations for APA are solved for the mixture as a whole. The conservation equations for FMF and CVA are solved for all fluids simultaneously. The nitric oxides are supposed to be presented only in trace quantities non-contributing to the state of fluids and within-fluid mass conservation.
For APA, the transport equations which govern their conservation are of conventional type. They are not desribed here.
The following formulations are used for:
The source terms featuring in the latter will now be presented in turn.Within-fluid enthalpy-source terms are defined as:
SH1,k = (RcomCH4,kH°CH4 + RcomCO,kH°CO)Fk
where
Within-fluid methane-source terms are calculated from the rate of combustion as:
SCH4,k = RcomCH4Fk
Within-fluid oxygen-source terms are defined via net rates as:
SO2,k = RnetO2,k Fk
Within-fluid carbon-dioxide-source terms are defined via net rates as:
SCO2,k = RnetCO2,kFk
Within-fluid carbon-monoxide-source terms are defined via net rates as:
SCO,k = RnetCO,kFk
Within-fluid water-vapour-source terms are defined via net rates as follows:
SH2O,k = RnetH2O,kFk
Within-fluid nitric-oxide-source terms are defined via formation rates as:
SNO,k = RNO,kFk
Combustion taking place within k-fluid is treated as a two-step irreversible chemical reaction of methane oxidation as follows:
Step 1: CH4 + 1.5 ( O2 + 3.76N2) = CO + 2H2O + 5.64N2
Step 2: CO + 0.5( O2 + 3.76N2 ) = CO2 + 1.88N2
The reaction rates of combustion are obtained as the limiting blend of a Arrhenius kinetics and eddy-dissipation rates:
RcomCH4,k = - min ( RaCH4,k, ReCH4,k ) and
RcomCO,k = - min ( RaCO,k, ReCO,k ),
where Rak and Rek, in kg/m3/s, are the kinetic and eddy-dissipation rates:
ReCH4,k = 4 RHO1 EP/KE
min( FUk, OXk/3)
ReCO,k = 4 RHO1 EP/KE
min( COk, OXk/0.57)
RaCH,k4 =
1.15 109RHO12e-24444/Tk
FUk-0.3OXk1.3
RaCO,k =
5.42 109RHO12e-15152/Tk
OXk0.25HOk0.5COk
The remaining rates are defined through associated stoichiometric coefficients:
Step 1:
R1O2,k =
3 RcomCH4,k
R1CO,k =
-1.75 RcomCH4,k
R1H2O,k =
-2.25 RcomCH4,k
Step 2:
R2O2,k =
0.57 RcomCO
R2CO2,k =
-1.57 RcomCO
The net rates of species generation are the balances of formation and combustion as appropriate:
RnetCH4,k =
RcomCH4,k
RnetCO,k = RcomCO,k +
R1CO,k
RnetO2,k =
R1O2,k +
R2O2,k
RnetCO2,k =
R2CO2,k
RnetH2O,k =
R1H2O,k
NOX formation is calculated 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 NOX formation rate within k-fluid, in kg/m3/s, is given by:
RNO,k = 2 RHO1 K1,k NN2k [O]k MNO/MN2
where MNO = 30 is NO molecular mass,
MN2 =28 is N2 molecular mass and
K1,k = 1.8 108e-38370/Tk,
stands for the reaction-rate constant for the forward
reaction:
N2 + O --> NO +H
The equilibrium O-atom concentration, [O]k, can be obtained from the expression:
[O]k = 3.97 105Tk-0.5 (RHO1 OXk/MO2) 0.5e-31090/Tk
wherein MO2 =32 is the molecular mass of oxygen.
The gas mixture density is computed from the ideal-gas law.
The fluid specific enthalpies are related to fluid temperatures, Tk, and fluid specific heat:
H1k = CP,kTk
The k-fluid specific heat, CP,k, is assumed to be equal for all gas species and is a function of fluid temperature as follows:
CP,k = 1059 + 0.25( Tk - 300 )
The population-average values of general fluid attribute, Fª, is computed as:
Fª= SFk Fk
The RMS of the attribute fluctuations is calculated as
RMSF = (S (Fª-F k)²Fk)½
The following boundary conditions are applied:
The plots show the distribution of temperatures, velocities and the gas/fluid compositions within the burner.
The results of single-fluid simulation of the same case are used for comparisons. The details of single-fluid case can be found here.
Pictures are as follows :
To procure steady monotonic convergence, "false-time-step" relaxation was applied to all dependent variables: the false time step was the order of the time of residence of fluid in typical cell. In addition, linear under-relaxation was applied to the pressure corrections and density.
Around 100 iterative sweeps of the calculation domain were required for reasonable convergence, by which is meant that the maximum residual was less than 0.1%.
The CPU time required for typical run, solving 50 and storing another 105 variables, on 20x15x1 grid was about 20 minutes on PC Pentium-650.
An extention of Multi-Fluid Model for simulating turbulent combustion was presented. The model utilises the solution for CVA to describe the behaviour of realistic chemistry in turbulent reactive flow together with the prediction of presence probability of material from the fuel-bearing stream on the grounds of one-dimensional descritisation of fluid population space.
The results appear qualitatively realistic and mixture temperatures, velocities and gas compositions are within the expected range. The energy and mass conservations are strictly maintained both within fluid and for the whole-population behaviour. The highly non-linear nature of reaction rates appears to be more realistically represented by population averaging rather than operating with the single-fluid mean values of conventional treatment.
All model settings have been made by PIL commands and PLANT settings of PHOENICS 3.4
The relevant Q1 file can be downloaded by clicking here.
