Chemistry /chemical time scales

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. 

The limiting case where the chemical time scales are all large compared with the mixing time scale r, i.e., the slow-chemistry limit, can be treated by a simple first-order moment closure. In this limit, micromixing is fast enough that the composition variables can be approximated by their mean values (i.e., the first-order moments (0)). We can then write, for example,... 

Recall that the Jacobian of S will generate Ny chemical time scales. In the equilibrium-chemistry limit, all Ny chemical times are assumed to be much smaller than the flow time scales. 

The Nr eigenvalues of the Jacobian of S,p will be equal to the Nr non-zero eigenvalues of the Jacobian of Sc. Thus, in the equilibrium-chemistry limit, the chemical time scales will obey... 

Spontaneous ignition and associated features of organic gases and vapours are a consequence of the exothermic oxidation chemistry discussed in Chapter 1, but the way in which events unfold is determined by the physical environment within which reaction takes place. The heat transfer characteristics are probably most important, as may be illustrated with respect to the different consequences of adiabatic and non-adiabatic operation in a CSTR (Section 5) [117]. The notion of adiabatic operation may seem remote from any practical application, but this idealized condition may be approached if the chemical time-scale is considerably shorter than the time-scale for heat losses. 

Under the quasisteady formulation of Eqs. 3.1-3.8 and 3.11, the characteristic time scales for heat conduction in the sohd substrate must be suliiciently longer than the characteristic convective, diflhisive, and chemical time scales of the reacting flow inside the channel. This ensures that at every time step the gaseous flow and chemistry equilibrate to the imposed, at every time step, solid wall temperature. Accordingly, the time step At must be longer than the characteristic convective, diflhisive and chemical time scales of the reacting flow, but short enough to accurately resolve the transient heat response of the solid. 

Gaspard P and Burghardt I (ed) 1997 XXth Solvay Conf on Chemistry Chemical Reactions and their Control on the Femtosecond Time Scale (Adv. Chem. Phys. 101) (New York Wiley)... 

Figure 5.1. Closures for the chemical source term can be understood in terms of their relationship to the joint composition PDF. The simplest methods attempt to represent the joint PDF by its (lower-order) moments. At the next level, the joint PDF is expressed in terms of the product of the conditional joint PDF and the mixture-fraction PDF. The conditional joint PDF can then be approximated by invoking the fast-chemistry or flamelet limits, by modeling the conditional means of the compositions, or by assuming a functional form for the PDF. Similarly, it is also possible to assume a functional form for the joint composition PDF. The best method to employ depends strongly on the functional form of the chemical source term and its characteristic time scales.

For elementary chemical reactions, it is sometimes possible to assume that all chemical species reach their chemical-equilibrium values much faster than the characteristic time scales of the flow. Thus, in this section, we discuss how the description of a turbulent reacting flow can be greatly simplified in the equilibrium-chemistry limit by reformulating the problem in terms of the mixture-fraction vector. 

Under the simulation conditions, the HMX was found to exist in a highly reactive dense fluid. Important differences exist between the dense fluid (supercritical) phase and the solid phase, which is stable at standard conditions. One difference is that the dense fluid phase cannot accommodate long-lived voids, bubbles, or other static defects, whereas voids, bubbles, and defects are known to be important in initiating the chemistry of solid explosives.107 On the contrary, numerous fluctuations in the local environment occur within a time scale of tens of femtoseconds (fs) in the dense fluid phase. The fast reactivity of the dense fluid phase and the short spatial coherence length make it well suited for molecular dynamics study with a finite system for a limited period of time chemical reactions occurred within 50 fs under the simulation conditions. Stable molecular species such as H20, N2, C02, and CO were formed in less than 1 ps. 

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