Combustion quasi-steady

Our treatment of chain reactions has been confined to relatively simple situations where the number of participating species and their possible reactions have been sharply bounded. Most free-radical reactions of industrial importance involve many more species. The set of possible reactions is unbounded in polymerizations, and it is perhaps bounded but very large in processes such as naptha cracking and combustion. Perhaps the elementary reactions can be postulated, but the rate constants are generally unknown. The quasi-steady hypothesis provides a functional form for the rate equations that can be used to fit experimental data. 

Thus, it should be noted that the flame propagation in combustible vortex rings is not steady, but "quasi-steady" in the strict sense of the word. This may explain why prediction 9, based on the momentum flux conservation can better describe the flame speed for large values of Vg than prediction 4, which adopts the Bernoulli s equation on the axis of rotation. 

Quintiere, J. G., McCaffrey, B. J. and DenBraven, K., Experimental and theoretical analysis of quasi-steady small-scale enclosure fires, in 17th International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pennsylvania, 1979, pp. 1125-37. 

An interesting approach to the spray problem has been suggested by Chiu and Liu [29], who consider a quasi-steady vaporization and diffusion process with infinite reaction kinetics. They show the importance of a group combustion number (G), which is derived from extensive mathematical analyses and takes the form... 

A reaction at the initial temperature changes the characteristics of an explosive mixture before the flame front and introduces an element of nonsteadiness into the process of propagation of the combustion wave. The method proposed in [1] to describe this effect consists in replacing the original non-steady problem by a quasi-steady one with adiabatically increasing initial temperature Ta(f) and an effective source of heat release which takes this increase into account. We test this method below by comparing it directly with the results of a numerical solution of the original non-steady problem. 

The dashed lines in Fig. 1 show the temperature profiles 0(t) for the quasi-steady problem superimposed on the actual values for the temperature 0t = (0C + 0a)/2, where 0C = 0 is the combustion temperature and 0a is the time-dependent temperature before the front. The close correspondence between the profiles (the difference is less than 10%) not only shows a good approximation to the exact solution, but also indicates the significant role of the half-sum of the temperatures as a reference coordinate of the flame, as was noted in [1],... 

The central thesis of the theory of the non-steady combustion of powders and explosives developed by Ya.B. in this article is the assumption of rapid readjustability of the gas phase of combustion compared to thermal changes in the condensed phase, which allows us to consider the gas phase as quasi-steady. This fundamental property of burning condensed materials allows us not only to significantly simplify the solution of the problem by reducing it to an analysis of the non-steady temperature distribution in the surface layer of the condensed material, but also not to carry out a detailed analysis of the complex structure of the combustion zone above the material (the multi-stage character of the chemical transformation, thermal decomposition, and gasification of the dispersed particles of condensed material and other processes). 

Let us consider the symmetrical burning of a spherical droplet with the radius rp in surroundings without convection. Assume that there is an infinitely thin flame zone from the surface of the droplet to the radial distance rn [137], which is much larger than the radius of the droplet, rp. The heat released from the burning is conducted back to the surface to evaporate liquid fuel for combustion. Because the reaction is extremely fast, there exists no oxidant in the range of rp< r < m while no fuel vapor is available at r > rn. At a quasi steady state the mass flux through the spherical surface with the radius r (>rp), Mfv, can be obtained with Fick s law as... 

Oince the earliest theoretical models by Spalding (I) and Godsave (2) describing the quasi-steady, spherically symmetric combustion of individual fuel droplets in quiescent atmospheres, numerous more elaborate theories have been proposed to provide a better understanding of droplet spray combustion. These theories are based on the premise that the physical and chemical processes involved dmmg single-droplet combustion are fundamental to complex spray combustion processes. 

Of the many extensions of the classical quasi-steady droplet combustion models, most have dealt with the nonsteady eflFects which take place during droplet ignition and combustion (3-9). Using Greens function techniques to evaluate the nonsteady heat and mass transfer equations... 

In keeping with the assumptions of the classical quasi-steady droplet combustion models by Spalding (I) and Godsave (2), the combustion process is assumed for this investigation to take place instantaneously at a fiame surface where the fuel and oxygen react stoichiometrically and completely. Then the rate at which fuel is reacted at a fiame surface located at r = b can be expressed in terms of the delta function by ... 

Upon substituting Equation 20 for the reaction rate of fuel into Equations 16,17, and 18 and performing the integrations, the quasi-steady gas-phase temperature and weight fraction profiles during ignition and combustion are found to be ... 

Group Combustion of Droplets in Fuel Clouds. I. Quasi-steady Predictions... 

Results for oscillatory combustion assuming quasi-steady gas and condensed phase reaction zone (surface reaction approximation) are presented in two groups. First, general characteristics of oscillatory combustion are discussed in the context of the non-dimensional formulation, similar to the steady-state benehmark problem of Table 1. Second, specific results for the common materials NC/NG and HMX are presented. 

This implies that the spray tends to approach a saturation state unless additional heat and oxygen are supplied from the outside of the spray stream. It also implies that the behavior of the outer diffusion flame dominates the subsequent evolution of spray combustion from the spray boundary side. In real spray combustion, this boundary-layer type of change occurs dynamically because the boundary of the spray stream is located in the coherent vertical structure of the shear layer. In addition, turbulent effects are inevitable. However, such fluid dynamic effects have not yet been well characterized. Therefore, we focus on the behavior of the outer diffusion flame based on a quasi-steady continuum spray model. Chiu s theory is developed on this basis to classify the combustion modes excited by the penetration of the outer diffusion flame into the spray region. 

M. Labowsky, D.E. Rosner Group combustion of droplets in fuel. Clouds, I. Quasi-steady predictions, in Evaporation-Combustion of Fuels (J.T. Zung, Ed.) American Chemical Society (1978), pp. 63-79. 

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