Combustion time scale

The second example of an air pollutant that affects the total body burden is carbon monoxide (CO). In addihon to CO in ambient air, there are other sources for inhalation. People who smoke have an elevated CO body burden compared to nonsmokers. Individuals indoors may be exposed to elevated levels of CO from incomplete combustion in heating or cooking stoves. CO gas enters the human body by inhalation and is absorbed directly into the bloodstream the total body burden resides in the circulatory system. The human body also produces CO by breakdown of hemoglobin. Hemoglobin breakdown gives every individual a baseline level of CO in the circulatory system. As the result of these factors, the body burden can fluctuate over a time scale of hours. 

It is necessary to calibrate the 14C time scale for greater dating accuracy. However, the second-order variations are at least as important as the first-order constancy of atmospheric 14C. For example, they provide a record of prehistoric solar variations, changes in the Earth s dipole moment and an insight into the fate of C02 from fossil fuel combustion. Improved techniques are needed that will enable the precise measurement of small cellulose samples from single tree rings. The tandem accelerator mass spectrometer (TAMS) may fill this need. 

In hindsight, the primary factor in determining which approach is most applicable to a particular reacting flow is the characteristic time scales of the chemical reactions relative to the turbulence time scales. In the early applications of the CRE approach, the chemical time scales were larger than the turbulence time scales. In this case, one can safely ignore the details of the flow. Likewise, in early applications of the FM approach to combustion, all chemical time scales were assumed to be much smaller than the turbulence time scales. In this case, the details of the chemical kinetics are of no importance, and one is free to concentrate on how the heat released by the reactions interacts with the turbulent flow. More recently, the shortcomings of each of these approaches have become apparent when applied to systems wherein some of the chemical time scales overlap with the turbulence time scales. In this case, an accurate description of both the turbulent flow and the chemistry is required to predict product yields and selectivities accurately. 

An example of a smart tabulation method is the intrinsic, low-dimensional manifold (ILDM) approach (Maas and Pope 1992). This method attempts to reduce the number of dimensions that must be tabulated by projecting the composition vectors onto the nonlinear manifold defined by the slowest chemical time scales.162 In combusting systems far from extinction, the number of slow chemical time scales is typically very small (i.e, one to three). Thus the resulting non-linear slow manifold ILDM will be low-dimensional (see Fig. 6.7), and can be accurately tabulated. However, because the ILDM is non-linear, it is usually difficult to find and to parameterize for a detailed kinetic scheme (especially if the number of slow dimensions is greater than three ). In addition, the shape, location in composition space, and dimension of the ILDM will depend on the inlet flow conditions (i.e., temperature, pressure, species concentrations, etc.). Since the time and computational effort required to construct an ILDM is relatively large, the ILDM approach has yet to find widespread use in transported PDF simulations outside combustion. 

If Da = 1 is defined as the transition between diffusionally controlled and kinetically controlled regimes, an inverse relationship is observed between the particle diameter and the system pressure and temperature for a fixed Da. Thus, for a system to be kinetically controlled, combustion temperatures need to be low (or the particle size has to be very small, so that the diffusive time scales are short relative to the kinetic time scale). Often for small particle diameters, the particle loses so much heat, so rapidly, that extinction occurs. Thus, the particle temperature is nearly the same as the gas temperature and to maintain a steady-state burning rate in the kinetically controlled regime, the ambient temperatures need to be high enough to sustain reaction. The above equation also shows that large particles at high pressure likely experience diffusion-controlled combustion, and small particles at low pressures often lead to kinetically controlled combustion. 

For some reactions the rate constant kj can be very large, leading potentially to very rapid transients in the species concentrations (e.g., [A]). Of course, other species may be governed by reactions that have relatively slow rates. Chemical kinetics, especially for systems like combustion, is characterized by enormous disparities in the characteristic time scales for the response of different species. In a flame, for example, the characteristic time scales for free-radical species (e.g., H atoms) are extremely short, while the characteristic time scales for other species (e.g., NO) are quite long. It is this huge time-scale disparity that leads to a numerical (computational) property called stiffness. 

Errors and confusion in modelling arise because the complex set of coupled, nonlinear, partial differential equations are not usually an exact representation of the physical system. As examples, first consider the input parameters, such as chemical rate constants or diffusion coefficients. These input quantities, used as submodels in the detailed model, must be derived from more fundamental theories, models or experiments. They are usually not known to any appreciable accuracy and often their values are simply guesses. Or consider the geometry used in a calculation. It is often one or two dimensions less than needed to completely describe the real system. Multidimensional effects which may be important are either crudely approximated or ignored. This lack of exact correspondence between the model adopted and the actual physical system constitutes the basic problem of detailed modelling. This problem, which must be overcome in order to accurately model transient combustion systems, can be analyzed in terms of the multiple time scales, multiple space scales, geometric complexity, and physical complexity of the systems to be modelled. 

The combustion reaction rate is controlled both by the availability of fuel and oxygen kinetic effects (temperature). In full-scale fire modeling, the resolvable length and time scales are usually much larger than those associated with the scales of the chemical combustion reaction, and it is common to assume that the reactions are infinitely fast. The local reaction rate depends on the rate at which oxygen and fuel are transported toward the surface of stoichiometric mixture fraction, shown in Figure 20.2 as a point where both oxygen and fuel mass fractions go to zero. For almost 20 years, the EBU or eddy dissipation models were the standard models used by the combustion CFD community. With the EBU, in its simplest form, the local rate of fuel consumption is calculated as [3] ... 

The form of EBU expression is mainly based on dimensional arguments. The ratio k/ is the turbulent time scale. If the turbulence intensity is high, so is the fuel consumption. For the prediction of secondary species, such as CO, HC1, and soot, more advanced models using flamelets [37] have been used. The flamelets (and state relations) can be determined either experimentally [39] or computationally, using detailed models for combustion chemistry [40] that incorporate strain rate effects. 

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

The primary research tools used in this program were C-E s Drop Tube Furnace System (DTFS), a bench scale entrained laminar flow furnace and the Controlled Mixing History Furnace (CMHF), a pilot scale entrained plug flow furnace. Both the DTFS and CMHF by virtue of their ability to resolve combustion time into distance along their respective furnace lengths were used to examine carbon burnout phenomena associated with the SRC and reference coals. In addition, the CMHF by virtue of its staged combustion capabilities was used extensively to evaluate N0X emissions and to establish conditions conducive to low N0X ... 

---