Turbulent flames heat release

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

To examine the effect of turbulence on flames, and hence the mass consumption rate of the fuel mixture, it is best to first recall the tacit assumption that in laminar flames the flow conditions alter neither the chemical mechanism nor the associated chemical energy release rate. Now one must acknowledge that, in many flow configurations, there can be an interaction between the character of the flow and the reaction chemistry. When a flow becomes turbulent, there are fluctuating components of velocity, temperature, density, pressure, and concentration. The degree to which such components affect the chemical reactions, heat release rate, and flame structure in a combustion system depends upon the relative characteristic times associated with each of these individual parameters. In a general sense, if the characteristic time (r0) of the chemical reaction is much shorter than a characteristic time (rm) associated with the fluid-mechanical fluctuations, the chemistry is essentially unaffected by the flow field. But if the contra condition (rc > rm) is true, the fluid mechanics could influence the chemical reaction rate, energy release rates, and flame structure. 

There are many different aspects to the field of turbulent reacting flows. Consider, for example, the effect of turbulence on the rate of an exothermic reaction typical of those occurring in a turbulent flow reactor. Here, the fluctuating temperatures and concentrations could affect the chemical reaction and heat release rates. Then, there is the situation in which combustion products are rapidly mixed with reactants in a time much shorter than the chemical reaction time. (This latter example is the so-called stirred reactor, which will be discussed in more detail in the next section.) In both of these examples, no flame structure is considered to exist. 

To expand on the understanding of the physical nature of turbulent flames, it is also beneficial to look closely at the problem from a chemical point of view, exploring how heat release and its rate affect turbulent flame structure. 

The values of laminar flame speeds for hydrocarbon fuels in air are rarely greater than 45cm/s. Hydrogen is unique in its flame velocity, which approaches 240cm/s. If one could attribute a turbulent flame speed to hydrocarbon mixtures, it would be at most a few hundred centimeters per second. However, in many practical devices, such as ramjet and turbojet combustors in which high volumetric heat release rates are necessary, the flow velocities of the fuel-air mixture are of the order of 50m/s. Furthermore, for such velocities, the boundary layers are too thin in comparison to the quenching distance for stabilization to occur by the same means as that obtained in Bunsen burners. Thus, some other means for stabilization is necessary. In practice, stabilization... 

Many practical industrial processes are diffusion limited (i.e., have a high Damkohler number), and the assumption that the chemistry is fast is often sufficient to predict the overall characteristics of the process. For instance, in turbulent diffusion flames, the rates of fuel oxidation and heat release are often governed by the turbulent transport and mixing. 

TURBULENT FLAME SPACE RATES AND SPACE HEATING RATES. Recognizing that turbulent flames cannot be uniquely characterized in terms of burning velocity, Simon and Wagner have recently described a new approach (66). The method has two advantages It requires no a priori assumption about the nature of the flame— whether it is folded or thickened, and it gives the space needed for burning and the rate of heat release in that space—both important in practical applications. 

In view of the results just given, we might guess that local average rates of chemical heat release in turbulent diffusion flames are calculable in some fashion from P(Z). However, this is not possible even in principle for equilibrium flows. As equilibrium is approached, the chemical production terms in the equations for species conservation become indeterminate, involving differences of large numbers that cancel (for example, see Section B.2.5.2). A more circuitous route is therefore needed to find the average rate of heat release [15], [20], [27], [28]. The necessary expressions will be developed here. 

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