B URNING V ELOCITY
3.2. MILD COMBUSTION
An ensemble of inlet variables and boundary conditions that determine which single or multiple processes exist within a reactor can be used to characterize the reactor and its operation. These variables can be expressed in terms of a vectorf:
f¼f(m_inleti ,Tiinlet,preactor,treactor), (3:1) where m_inleti and Tiinlet are the mass flow rate and temperature of the reactants and diluents, respectively,preactoris the pressure inside the reactor (under the assumption of quasi-isobaricity), andtreactoris the average residence time. Note that thisfis not the equivalence ratio, as it denotes in other chapters of this book.
Figure 3.1 presents a schematic overview of a reactor. Oxidants, fuels, and diluents flow into the reactor with mass flow rates m_ox, m_fuel, and m_dil, respectively, and with temperaturesTox, Tfuel, andTdil. It should be stressed that the diluent flow can be either
fed to the system as a separate stream or premixed with the other flows. In the latter case, oxygen and fuel molar fractions in the oxidant and fuel streams, respectively, are lower than unity.
When the variable vector is known, it is possible to define a number of synthetic quantities that can be used to classify processes taking place in the reactor. The average inlet temperature,Tinlet, is the average of all the inlet temperatures weighted by their corresponding mass flows and heat capacities. Another way to identify the system status is by means of its frozen mixture temperature,Tfroz(Z), which represents the tempera- tures of all possible frozen mixtures consistent with the inlet conditions. In premixed systems, the two quantities coincide because only one inlet temperature can be fixed, whereas in reactors in which fuels, oxidants, and sometimes diluents are fed separately, the two temperatures can be different. The average inlet temperature is easy to calculate even in the presence of multiple flows. The frozen mixture temperatures depend on the mixture fractions, which depend in turn on the number of inlet flows. In practice, a great number of processes utilize flows of fuel and oxidant in which one or both of these streams are diluted. In this case, it is possible to define a simple mixture fraction that varies between 0 and 1 (Cavaliere and Ragucci, 2001). The temperature associated with this mixture is the average temperature weighted by the composition of the mixture, and is therefore a function of the composition (i.e., of the mixture fraction).
Other quantities of interest are the autoignition temperature of the system,TIGN, and the mixture autoignition temperature, Tign(Z). These are the temperatures at which minimum conversion occurs starting either from the average composition, or from a frozen mixture consistent with the inlet flows for a period shorter than the residence time of the reactor. Finally, the maximum temperature, Tmax(Z), is defined as the temperature achievable for the maximum oxidative or pyrolytic conversion of a mix- ture,Z, consistent with the reactor conditions.
It is important to understand the meaning and the usefulness of these temperatures.
Combining the temperatures forms a maximum temperature increase, DTMAX, and a maximum ignition–inlet differential,DTIGN. The maximum temperature increase is the greater of two maxima evaluated by means of Equations (3.2) and (3.3):
DTMAX¼max½Tmax(Z)Tfroz(Z) for TeqðZÞ> TfrozðZÞ, (3:2) DTMAX¼max½Tfroz(Z)Teq(Z) for TeqðZÞ> TfrozðZÞ: (3:3) The first maximum is defined by the greatest difference between maxima for TeqðZÞ>TfrozðZÞ, and is between the frozen mixture maximum temperature and the inlet frozen mixture temperature according to Equation (3.2). The second maximum is for the difference between the mixture frozen temperature and the mixture equilibrium tempera- tureTeq(Z) according to Equation (3.3) that is generally referred to pyrolytic conditions.
Tfuel , Tox , Tdil ,
mfuel
mproduct
moxid
τ , p mdil
•
•
•
•
Figure 3.1 Schematic overview of a reactor.
The maximum temperature increase is a measure of the possible incremental temperature increase or decrease that the process can experience, and is related to exothermicity and endothermicity as well as to the mass of the inert in which the reaction products are mixed. Nearly isothermal processes develop when the maximum temperature increase is around zero, whereas oxidation and pyrolysis take place when this quantity is positive or negative, respectively.
The differential inlet–ignition temperature is the maximum difference between the inlet frozen mixture temperature and the autoignition frozen mixture temperature according to Equation (3.4):
DTINLET¼max½Tfroz(Z)Tign(Z): (3:4)
In this case, the difference represents the tendency of the system to undergo explosion or autoignition. That is, the reactants introduced in the reactor can evolve along a reaction path without additional heating from an external source.
The combination of the two difference values identifies regimes which are well known as large macro-area processes. They are reported in Figures 3.2 and 3.3. The first figure identifies four broad categories on a diagram in which the maximum temperature difference and the inlet–ignition differential are reported on the ordinate and abscissa axes, respectively. The upper left quadrant is the region of assisted-ignited combustion for which the maximum temperature difference is positive compared to the inlet–
ignition differential, which is negative. This is the classical combustion condition in which ignition of the mixture is ensured by heat introduced externally to the reactor, because the reactants do not carry enough sensible enthalpy to initiate the process.
Processes located in the upper right quadrant of the figure are classified as autoignited combustion. In this case, the inlet–ignition differential temperature is positive, so ignition occurs spontaneously. Beneath the abscissa, the processes are characterized by a negative maximum temperature increase. These processes are referred to as pyrolysis because they are endothermic in nature. Pyrolysis is subdivided into two categories: autoincepted pyrolysis and assisted-incepted pyrolysis. Autoincepted pyr- olysis does not need an external source to make the processes effective. It is defined by the lower right quadrant of Figure 3.2. Assisted-incepted pyrolysis needs external heating or a catalytic device in order to develop. It is defined by the lower left quadrant of the figure where the inlet temperature is lower than the ignition temperature. In the case of pyrolysis, this inlet temperature should be named the inception temperature.
∆TMAX
∆TINLET
Autoincepted pyrolysis Autoignited combustion Assisted-ignited
combustion
Assisted pyrolysis
Figure 3.2 Combustion regimes on a temperature plot. The maximum temperature increase of a process is reported on the ordinate, and the inlet ignition temperature difference is reported on the abscissa.
This broad classification can be refined by means of comparison between two differentials, that is the maximum temperature increase DTMAX of the equation (3.2) and the standard autoignition temperature difference DTIGNo , which is the difference between the autoignition temperature at the stoichiometric air–fuel mixture fraction, and the temperature in standard conditions,To, according to Equation (3.5):
DTIGN0 ¼Tign0 To: (3:5)
Figure 3.3 reports the possible subregimes which can be identified when the max- imum temperature increase is higher or lower than the standard autoignition temperature differential. Specifically, the region under the horizontal line in the assisted-ignited combustion quadrant on the left side identifies conditions in which no combustion process should occur. This is the region in which the maximum temperature increase is still lower than the temperature increment needed to activate the processes even in a hot diluted system. Therefore, reaction is not assured to take place in a diluted system. The only possible processes under these conditions are those that develop when an external aid, which lowers or overcomes the activation energy of the processes, is added (i.e., catalytic assistance or external heat addition). It is appropriate that this category be named pilot combustion. In the upper part of the quadrant, all the processes recognized in classical combustion (Williams, 1985; Kuo, 1986; Griffiths and Barnard, 1995;
Peters, 2000) as deflagration, detonation, or diffusion flames are reported. They are called feedback combustion processes because the enthalpy of the combustion products can heat the reactants up to a temperature that allows oxidation to occur.
Finally, the right quadrant of Figure 3.3 is subdivided into fields named HiTeCo or HiTAC, and MILD combustion. All of these are characterized by autoignition of the mixture by means of the sensible enthalpy carried by the reactants themselves, but they differ since the maximum temperature increase can be higher or lower than the standard ignition temperature differential.
Understanding the subdivision between HiTeCo and MILD combustion is useful in order to stress that the oxidation process is under the control of either the temperature of the reactant flows, or of the temperature which develops during combustion. This distinction is easy to understand in the limiting cases where the maximum temperature increase is much higher or lower than the temperature for autoignition; in this case the ratio of maximum to autoignition temperatures then tends to infinity or zero. In the particular case where the ratio is around unity, however, the reactive structure is located in the same region for HiTeCo and MILD combustion. Here, oxidation is driven by the
Feed-back combustion
Pilot
combustion MILD
combustion
∆TMAX
∆TI O GN
∆TINLET
High-temperature combustion
Figure 3.3 Non-pyrolytic combustion regimes subdivided on the ordinate of Figure 3.2.
enthalpy content of the reactants or by the enthalpy released during the reaction. This is not a general rule, and the transition may occur at different values of the temperature ratio, as can occur when the reactive structure is positioned in different regions and is under the control of different factors.