The physical problem
The application considers the combustion of volatiles emerging from finely dispersed solid fuel in a particular 2D combustor with flow reversal.
It is assumed that solid fuel volatilization causes the consumption of (raw) solid fuel, and the appearance of ash (in the solid particle) and volatiles (in the gas). The volatile is taken as methane, CH4.
Whereas the volatile combustion is supposed to proceed in accordance with the "mixed-is-burned", SCRS, rule, the volatile-generation reaction is supposed to be kinetically controlled.The local and instantaneous volatile-generation rate is taken to be a particular function of temperature.
The study shows that the total volatile-production rate is predicted to have a magnitude which is quite different when the fluctuations are taken into account from what they are not. As a consequences, the predictions of overall performance of the combustor by way of "standard" single-fluid model may be far away from being realistic.
Case considered
The present case consists of an axi-symmetric burner with restricted exhaust in which the solid-fuel fines burn in a stream of heated air. The solid-fuel fines premixed with the certain amount of primary air are introduced through a pipe on the symmetry axis of the burner, and the secondary air is introduced through an annular inlet surrounding the fuel pipe as depicted here.
Modeling details
The present treatment of two-phase flow is based on the homogeneous approach considering no slip velocity and no temperature difference between the solid and gas phases. It is assumed that there is no influence of particles on the turbulence structure represented via standard K-e model of turbulence.
Solved-for variables:
V1, W1, P1, KE, EP, H1, YCOA, YASH, MXFV, YN2 - for single-fluid model and
additionally F1, F2, ....., F21 - for 21-fluid MFM.
Composition mass fractions:
Volatilisation model
1kg Solid Fuel -> Yvol kg Volatiles (CH4) + (1-Yvol)kg Ash
Yvol is obtained from the initial solid fuel composition.
Main features of combustion model
For the solid fuel, raw material, YCOA, is consumed during devolatilisation, and inert ash appears as YASH and increases its content.
Volatile fuel, YCH4, appears as a consequence of volatilisataion, and then dissappears as it is burned consuming oxygen, YO2.
Volatiles combustion model
CH4 + 2O2 -> CO2 + 2H2O + Hch4, where
Hch4 is the heat of combustion for methane.
Combustion is treated as a single-step irreversible diffusion-controlled chemical reaction with a infinitely fast rate between volatile fuel and oxygen. The gas composition and its enthalpy are related to the mixture fraction according to the Simple Chemical Reaction Scheme, SCRS, concept as follows:
Mixture fraction of fuel volatile substance is defined as:
MXFV = (s×YCH4-YO2+1)/(1+s), where
s = 4 as stoichiometry of O2 consumption dictates.
MXVF is supposed to appear with volatilisation rate.
The mass fractions of oxygen and methane are then calculated:
YCH4=AMAX1(0.,(MXFV-MXFVst)/(1.-MXFVst) and
YO2 =AMAX1(0.,1.-MXFV/MXFVst), where
MXFVst=1/(1+s)
Note: the above treatment should not be considered as an accurate one; for, in reality, the stoichiometry must reflect the diluted nature of oxidant in either streams. However, the comparative analyses are often tolerant of certain, but consistently applied, modeling inadequacies.
In contrast to single-fluid approach, an equation for MXFV is not used. Instead, each fluid of multi-fluid population is assumed to have its own mixture fraction and appropriate composition, i.e. individual contents of oxygen and volatile fuel, governed by within-fluid SCRS.
Further, the mixture fraction is supposed to be uniformly distributed, in the range from zero, volatile-free fluid, to unity, oxygen-free fluid, between all fluids. The frequency in population is then calculated for each fluid by solving built-in fluid-mass-fraction equation.
Statistically averaged values of YO2 and YCH4 of the fluid population are finally deduced.
For single-fluid treatment
VRAT=2000.×Yvol×YCOA×e-2829/TMP1
The appropriate source/sinks are introduced for all the fluids of multi-fluid population.
Density and specific heats
Ideal-gas law is used for the density of gas components with solid density and all specific heats taken as constant.
Temperature calculation
Linear total-enthalpy-temperature relationship is employed, with a constant heat of combustion.
Simulation results
The results of the calculation will be presented by way of vectors and contour fields allowing the comparison to be made between single- and multi-fluid predictions, as follows:
This is because the mixture at any location consists of a population of fluids, each having its own values of:
Their distributions will be shown in the next figures.
Typical fluid-population mass fractions:
The present application has introduced MFM method for calculation of two-phase mixing and combustion triggered off by volatiles emerging from raw solid fuel.
The comparisons between single-fluid and multi-fluid simulations have shown the significant effect of the composition fluctuations on the devolatilization rate and resulting combustion.
Further research is needed to validate the results of this method and to determine to which extent the different assumptions are valid.
